Atlas home || Conferences | Abstracts | about Atlas
Host: University of Aarhus
Sponsor: The Danish National Research Foundation
Homepage: http://www.maphysto.dk/events/VogelCAC2000/
Email: maphysto@maphysto.dk
Organizers: Jørgen Ellegaard Andersen
Description:
Concentrated Advanced Course on Vassiliev invariants, chord diagrams, the Kontsevich integral, the structure of the algebra of Feynman diagrams, and the universal Lie algebras
Vassiliev theory:
Invariants of knots or links, Vassiliev invariants, singular links and chord diagrams. The Vassiliev filtration on the space of
links and its relation with the module of chord diagrams.
Trivalent Feynman diagrams:
The AS and IHX relations. Basic facts about modules of trivalent diagrams ${cal A}(Gamma,X)$.
The Kontsevich integral:
Description of the integral. The isomorphism (after completion) between the modules of knots and the graded modules
of trivalent diagrams ${cal A}(S^1,emptyset)$.
Structure of the module ${cal A}(Gamma,X)$:
Coalgebra structure and functoriality. The algebra $Lambda$ and its action on modules of diagrams. Weight functions
coming from Lie algebras. The height characters corresponding to all Lie algebras and Lie superalgebras.
The universal Lie algebra:
Construction of this universal object. Known facts and conjectures about it: the category of representations, simple
modules and their dimensions.
Speakers: Pierre Vogel (Paris VII)
Date received: November 05, 1999, revised July 17, 2004
© 2008 Atlas Conferences Inc.